I should first make clear that I'm certainly no expert, and I'm struggling to understand this as much as you are.

Also, in the Brownian motor link, I'm not at all sure what they mean by that 'hurricane' sentence. The Science paper (reference 1 on the Wikipedia page) has a much clearer explanation of what happens at this scale (see below).

Having said that, I also think I was wrong in what I said before: assuming that the gradient would produce something approximating a linear flow, then the shape of the vanes would matter. It would, as you said, be more efficient in the direction shown in the video; reversing the gradient -- in effect reversing the flow so that it hits the angled slope -- would result in less net torque being transferred to the wheels. (Although I still think they'd rotate; just not as fast)

But I'm still not sure if any of this means that it's intrinsically easier for the wheels to rotate in one direction and not the other. Consider this: if one of these wheels were in an environment with random thermal noise, the net rotation would be zero, right? But it would jiggle clockwise and anticlockwise a bit because of random thermal noise. If the wheel could rotate more easily in one direction, then after a while it would end up spinning in that direction. And since that doesn't happen, I have to conclude that it must spin equally easily in either direction. (There may well be errors in my reasoning, in which case please advise!)

And yes, the video looks exactly like the clouds of bacteria are in random motion: there's no visible evidence of a gradient or a flow except for the fact that the wheels actually turn. But if there's really no gradient then I can't see how this works at all. What are we even looking at here? Is the video shot in real time? Are those smudges actually the coherent clouds of bacteria or just some kind of artifact? Where's the source of the oxygen? Damn it, I need to see the paper! These premature press releases and Youtube videos(!!) are very frustrating.

Meanwhile, in case you can't access the Science paper, here are three pretty good paragraphs from the introduction: (with apologies for the copypasta)

A small particle in a liquid is subject to random collisions with solvent molecules. The resulting erratic movement, or Brownian motion, has been described theoretically by Einstein (1) and independently by Langevin (2). Langevin hypothesized that the forces on the particle due to the solvent can be split into two components: (i) a fluctuating force that changes direction and magnitude frequently compared to any other time scale of the system and averages to zero over time, and (ii) a viscous drag force that always slows the motions induced by the fluctuation term. These two forces are not independent: The amplitude of the fluctuating force is governed by the viscosity of the solution and by temperature, so the fluctuation is often termed thermal noise.

At equilibrium, the effect of thermal noise is symmetric, even in an anisotropic medium. The second law of thermodynamics requires this: Structural features alone, no matter how cleverly designed, cannot bias Brownian motion (3, 4). To illustrate this point, Feynman discussed the possibility of using thermal noise in conjunction with anisotropy to drive a motor in the context of a "ratchet and pawl" device shrunk to microscopic size (4). He showed that when all components of such a device are treated consistently, net motion is not achieved in an isothermal system, despite the anisotropy of the ratchet's teeth. However, a thermal gradient in synergy with Brownian motion can cause directed motion of a ratchet and can be used to do work. As a practical matter, large thermal gradients are essentially impossible to maintain over small distances. Particularly in biology and chemistry, the thermal gradients necessary to drive significant motion are not realistic.

It might seem then that, despite its pervasive nature, Brownian motion cannot be used to any advantage in separating or moving particles, either in natural systems (such as biological ion pumps and biomolecular motors) or by artificial devices. Recent work has focused, however, on the possibility of an energy source other than a thermal gradient to power a microscopic motor. If energy is supplied by external fluctuations (5-8) or a nonequilibrium chemical reaction (9, 10), Brownian motion can be biased if the medium is anisotropic, even in an isothermal system. Thus, directed motion is possible without gravitational force, macroscopic electric fields, or long-range spatial gradients of chemicals.

(Nanowerk News) To make thin films for semiconductors in electronic devices, layers of atoms must be grown in neat, crystalline sheets. But while some materials grow smooth crystals, others tend to develop bumps and defects – a serious problem for thin-film manufacturing. In the online edition of the journal Science (Jan. 22, 2010), Cornell researchers shed new light on how atoms arrange themselves into thin films. Led by assistant professor of physics Itai Cohen, they recreated conditions of layer-by-layer crystalline growth using particles much bigger than atoms, but still small enough that they behave like atoms.